Magnetic tracking system

ABSTRACT

The present invention provides an electromagnetic tracking system that includes a field generator and a field sensor arranged to generate and detect, respectively, an electromagnetic field. Both the transmitter and receiver coils are connected to signal conditioning and processing circuitry to provide outputs indicative of the coil signals. A processor operates on the signals to determine the coordinates of the sensing assembly relative to the generator assembly. The signal processor produces ratiometric outputs, and applies a mutual inductance model to solve for position/orientation coordinates. In some embodiments, a disturber in the form of a conductive ring or a sheath is disposed about an interfering piece of equipment to moderate and standardize disturbances due to eddy currents.

BACKGROUND OF THE INVENTION

[0001] The present invention relates to magnetic tracking systems of thetype wherein a magnetic field is established in a relevant work area,and one or more magnetic field sensors are operated to sense values of alocal magnetic field and are processed to determine the position of atool, instrument or other identified object. In general, such systemsoperate using a field generating element or assembly, and a fieldsensing element or assembly, often in conjunction with other positiondetermining elements, such as robotic stepper or optical trackerassemblies to track the relative changes in position between one or morefixed points or structures in the physical environment or associatedimages, and one or more moving or non-visible points or structures inthe work arena.

[0002] Magnetic field generating or sensing assemblies for tracking maybe implemented in various ways, with conventional analog wire coilsforming current loops or paths, or with semiconductor ormicrolithographically-formed conductive leads or circuit board tracesforming current paths, arranged in an appropriate geometry to generateor sense the desired field components. There may be a symmetry orduality between the generating or sensing elements. Thus, for example inmany cases it is possible to have a small multi- coil array thatgenerates a spatially distributed magnetic field and a similar or evenidentical array that senses the field so generated. Small coils offerthe prospect of generating, to a close approximation, dipole fields,although small size may limit the attainable field strength or theachievable level of detection signal amplitude. The generating andsensing constructions may alternatively employ different scales, forexample, with relatively large and/or high current coils to establishmagnetic field components along different axes, and smaller, or morelocalized coil assemblies for sensing field values. Smaller coils,whether for sensing or generating, may, for example, be fastened to thebody, or attached to workplace or surgical instruments, or to cathetersor other body-inserted devices, to sense the magnetic field and trackposition of the attached structure.

[0003] In general, it is the aim of such magnetic tracking assemblies todefine the spatial coordinates (e.g., position and orientationcoordinates, either absolute or relative) where the movable magneticassembly is located at a given instant in time. It is thereforenecessary to characterize the magnetic field distribution or signalvalues with some degree of accuracy, and also necessary to accuratelydetect the field. The field distribution may be determined by acombination of field modeling and empirical field mapping. The latter,for example, may be carried out as a calibration or an initializationstep, and may be performed to correct a theoretical field distributionfor the presence of interfering structures. In any case, the spatialcoordinates are generally computed for one magnetic assembly(transmitter or sensor) with respect to the other magnetic assembly(sensor or transmitter). Typically, one of these assemblies is itselffixed.

[0004] One area in which magnetic tracking has been useful is the areaof image guided surgery. Typical image guided surgical systems acquire aset of images of an operative region of a patient's body, and track asurgical tool or instrument in relation to one or more sets ofcoordinates, e.g., spatial coordinates of the surgical work arena, thecoordinates of the images themselves, or a target feature of thepatient's anatomy. At the present time, such systems have been developedor proposed for a number of surgical procedures such as brain surgeryand arthroscopic procedures on the knee, wrist, shoulder or spine, aswell as certain types of angiography, cardiac or other interventionalradiological procedures and biopsies. Such procedures may also involvepre-operative or intraoperative x-ray images being taken to correct theposition of and refine the display of, or otherwise navigate a tool orinstrument involved in the procedure in relation to anatomical featuresof interest.

[0005] Several areas of surgery have required very precise planning andcontrol. Such tracking is useful for the placement of an elongatedprobe, radiation needle, fastener or other article in tissue or bonethat is internal or is otherwise positioned so that it is difficult toview directly. For brain surgery, stereotactic frames may be used todefine the entry point, probe angle and probe depth to access a site inthe brain. Furthermore, many of the foregoing techniques may be used inconjunction with previously-compiled three-dimensional diagnostic imagessuch as MRI, PET or CT scan images to provide accurate tissuecoordinates to which the tracked physical elements may be referenced.Such systems offer valuable improvements for procedures such asplacement of pedicle screws in the spine, where visual and fluoroscopicimaging directions cannot capture the axial view that would be requiredto safely orient the insertion path through bony material close to thespinal cord.

[0006] When used with existing CT, PET or MRI image sets, the previouslyrecorded diagnostic image sets, by virtue of their controlled scanformation and the spatial mathematics of their reconstructionalgorithms, define a high precision three dimensional rectilinearcoordinate system. However, even when provided with such referenceimages it is necessary to correlate and fit available measurement andviews and anatomical features visible from the surface, with features inthe diagnostic images and with the external coordinates of the toolsbeing employed. This is often done by providing implanted fiducials, byadding external visible or trackable markers that may be imaged, and byenabling a surgeon or radiologist to use a keyboard or mouse to identifyfiducials or features in the various images, and thus map common sets ofcoordinate registration points in the different images. Given a fit ofspatial points to image points, software may then track changingpositions in an automated way (for example, simply transforming thecoordinates that are output by an external coordinate measurementdevice, such as a suitably programmed off-the-shelf optical trackingassembly.) Instead of correlating image positions of a set of imageablefiducials appearing in fluoroscopic or CT images, such systems can alsooperate with simple optical tracking, employing an initializationprotocol wherein the surgeon touches or points at a number of bonyprominences or other recognizable anatomic features in order to definethe external coordinates in relation to the patient anatomy and toinitiate software tracking of those features.

[0007] For such applications, electromagnetic tracking offers theadvantage that its position-defining field, a magnetic field, penetratesthe body without attenuation or change so that tracking may continueduring a surgical procedure, unimpaired by the blocking that occurs withvisible light trackers (e.g., due to operating room personnel movinginto positions that obstruct the line-of-sight paths required by opticaltrackers). Optical or ultrasonic tracking, by contrast, may require alarger or excess number of line-of-sight paths, and correspondingtransponders and/or detectors to assure that triangulation is alwayspossible despite occluded pathways. The body-penetrating electromagneticfields also allow one to track locations or movements inside the bodywith minimal resort to the fluoroscopic or ultrasound techniquesnormally required for visualization.

[0008] Among electromagnetic tracking techniques, several principalapproaches are known. In one, relatively large Helmholtz coils establishwell defined and highly uniform independent magnetic field components orgradients along each of the X, Y and Z axes in a work arena, and thestatic field components are detected by a localized detector todetermine position coordinates. This approach has been proposed, forexample, for cranial surgery, where such coils may define a suitablylocalized region encompassing the entire operative arena. Anotherprincipal approach involves using time-varying dipole fields e.g.,dipole fields established by driving field-generating coils with an ACcurrent signal. While the latter approach offers some processingadvantages (such as being able to synchronously demodulate inducedsignals, and thus cumulate detected signal values to enhancesensitivity, and also the ability to establish the X, Y and Z fieldcomponents at different frequencies so that detected sensor outputsignals may be separated or even demodulated simultaneously), it has thedisadvantage that varying magnetic fields induce eddy currents inconductive structures found within the field. Induced currentsthemselves then generate secondary magnetic fields, thus introducingdistortions into the expected or calibrated field distribution.Conductive or metal structures are in fact commonly present in atracking environment, whether it be an avionics, surgical or industrialtracking environment.

[0009] The latter problem has historically been addressed by theobservation that for a fixed metal disturber located at least twice asfar from the field generator as is the field sensor, the induceddisturbance will be low, e.g., under one percent, so that by restrictingthe tracked arena to a region sufficiently removed from the disturbingstructure, accuracy may be achieved. However, this approach may beunrealistically restrictive for certain applications, including someimage guided surgery applications, where highly disturbing equipment(such as the imaging assembly of a fluoroscope) is necessarily placed asclose as possible to the work arena in which tracking is to occur.Another common alternative approach would be to map the disturbed fieldsor detected signal levels that occur close to the distorters present inthe work arena, so that a processor can more accurately determinecoordinates from the run time field values or the induced signalsdetected by a sensor. However, as a practical matter, such mapping isnot only likely to require a time-consuming preliminary set-upoperation, but may require that the set-up be carried out afresh foreach new arrangement of operating room equipment that introducesdifferent distortions, i.e., when equipment is changed or moved.

[0010] In addition to the practical problem of accurately detecting thefield, there is the theoretical problem of converting the signalmeasurements into position and orientation coordinates.

[0011] On a fundamental level, the task that must be addressed by anyelectromagnetic tracking system is to computationally determine a uniqueposition from the various measured parameters (typically inducedvoltages indicative of field strength). Often the relevant equationshave several solutions, and care must be taken to operate within asingle-valued domain (typically a hemisphere, quadrant or octant), thuslimiting the selection of the initial generator or receiver fixedlocations to establish a sufficiently well behaved field region, andrestricting the allowable work arena in relation thereto, or elseproviding additional, or extrinsic data inputs to resolve ambiguities orrefine computations. Beyond encountering multi-valued coordinatesolutions, the accuracy of the coordinate determination processing maydepend quite critically on the relative positions of generating andsensing elements. Processing equations may break down or solutions maybecome poorly defined as the sensing or generating element approaches orcrosses a particular plane or axis, or one of its pitch, yaw or rollangle coordinates approaches 0 or 90 degrees, becomes too acute, orbecomes too oblique.

[0012] Another practical problem stems from the dynamic range of thesensed signals, which varies greatly with distance/position, and maydrop to quite low levels with increasing distance from the transmitter,or with decreasing size of the generating or sensing coils. Often, as afield unit moves to different positions, different gains must bedetermined on the fly, or additional gain stages must be used in orderto obtain adequate signal values. This introduces some complexity andpotential for error in normalizing the signals to accurately fittogether readings from two different or even closely contiguous regions.

[0013] Thus, while magnetic tracking offers certain significantadvantages, particularly for surgical applications, there remains a needfor improved systems and processing to enhance accuracy of coordinatedeterminations.

[0014] Accordingly, it would be desirable to provide an electromagnetictracker of enhanced accuracy.

[0015] It would also be desirable to provide an electromagnetic trackerhaving enhanced immunity to common field distortions.

SUMMARY OF THE INVENTION

[0016] One or more of these and other desirable features are obtained inan electromagnetic tracking system wherein a field generating unit and afield sensing unit are arranged to generate and to sense, respectivelyan electromagnetic field in an arena of interest. At least one of theunits is movable, and the units are connected to signal conditioning andprocessing circuitry that detects the levels of the transmitter drivesignals and the received signals, ratiometrically combining them to forma matrix representative of the mutual inductance of each of the pairs ofcomponent coils. The mutual inductance information, providing functionsof the relative positions and orientations of the two units, is thenprocessed to determine corresponding coordinates.

[0017] Since mutual inductance is a symmetric property, i.e., dependingsimply on the geometries of the transmission and receiving coils andtheir relative positions, the system may interchange transmitter andreceiver units, employing quite small coil assemblies, yet use a modelthat gives a direct computation of coordinates without excessiveiterative approximations, and without resort to the multitude of gainlevel and other normalization corrections otherwise typically neededwhen working from magnetic field intensity measurements. The equationsmay be processed and solved in real time to effect surgical or otherposition tracking, and various corrections and calibration of signalmagnitude (e.g., for cross-coupling of coils or for finite-size andnon-circular coil geometries) are readily implemented.

[0018] In accordance with another aspect of the invention, the magnetictracking systems of the invention may employ signal conditioning orprocessing electronics in which relevant signals pass through fixed gainamplifiers to high precision (e.g, 24 bit A/D) digital converters. Thisbit size encompasses a dynamic range effective for multi-bitrepresentation of signals encountered at all regions of the intendedtracking area, thereby avoiding the need for variable gain or AGCelements, or for multiple or different preamps having different gainlevels, as one coil assembly moves further from the other. Thus, theprovision of a common preamplifier with a high precision samplereliminates patching and the errors due to inaccurate gain ratios betweengain states.

[0019] In accordance with another or further aspect of the invention,the processor employs a model or set of equations that operate, with thesensor output values, to determine the position/orientation coordinatesof the transmitter/receiver assemblies, and when a tracked magnetic coilassembly element approaches a singular region, i.e., a plane or regionwhere the model becomes ill-defined, inaccurate or lacks a solution inthe coordinate system, the processor operates by transforming to acoordinate representation in which the detected values lie in awell-defined or non-singular region. The processor then solves todetermine a coordinate measurement, and transforms back to theunderlying or original coordinate system.

[0020] In accordance with another aspect, an operating room system ofthe invention may employ a conductive shield, or a sheath structureconfigured to fit about or contain an interfering component or piece ofequipment. The sheath standardizes the magnetic field disturbanceintroduced by the component. In some instances the sheath may be a metalcylinder, dimensioned to enclose the disturbing piece of equipment. Thesheath or cylinder may be formed of sheet metal of a gauge such thateddy currents are induced by the magnetic field, thus giving rise to astandardized field disturbance originating at a contour or surfaceexternal to the equipment. Alternatively, other suitable conductivematerials, such as a carbon fiber composite material, may be used. Thesheath also moderates or effectively nulls electromagnetic disturbancesoriginating within its contour, e.g., at the underlying piece ofequipment disposed within the sheath. The inclusion of this standardizeddisturbance in a system of the invention permits the interchange ofdifferent pieces of equipment without introducing excessive variationsin resulting local disturbance characteristics. Disturbances may thus bemapped, or even modeled, in a single initial set up operation, withoutnecessitating compilation of a new disturbance map for each new piece ofequipment

[0021] In accordance with another or additional aspect of the invention,rather than simply introducing a sheath to form a standardizeddisturbance, the processor may model such a disturbance. For example,the processor may model a conductive sheath fitted about a certainregion as a conductive ring or cylinder at that region (using the knowndimensions and behavior characteristics of the sheet metal material).The modeled disturbance may then be added to the stored values of a mapof the undisturbed electromagnetic field to form an enhanced field map,or may be otherwise applied to enhance accuracy of trackingdeterminations. The modeled field may also be used to provide a seedvalue for determining position and orientation coordinates. A fittingprocedure then refines the initial value to enhance the accuracy of theP&O determination.

BRIEF DESCRIPTION OF THE DRAWINGS

[0022] These and other features of the invention will be understood fromthe description below and accompanying claims, taken together with theFigures illustrating embodiments thereof wherein:

[0023]FIG. 1 illustrates basic hardware elements of a tracking system inaccordance with the present invention;

[0024]FIG. 2 is a hardware block diagram of a preferred embodiment;

[0025]FIG. 3 is a high level flow chart illustrating operation of asystem according to one aspect of the invention;

[0026]FIG. 4 illustrates signal processing for determining coordinateswith the system of FIG. 3;

[0027] FIGS. 5A-5F illustrate circuit details of some exemplaryembodiments;

[0028]FIG. 6 illustrates aspects of distortion correction in accordancewith other aspects of the invention;

[0029]FIG. 7 is a network model of the system of FIG. 6;

[0030]FIG. 8 illustrates geometry of fields for the configuration ofFIG. 7;

DETAILED DESCRIPTION

[0031] The present invention is an improved electromagnetic trackingsystem which may, by way of example, be employed in an operating room orclinical setting to determine the position and orientation of an objectsuch as a catheter, surgical tool, marker or the like in relation toother physical structures, or in relation to images that may, forexample, have coordinates assigned thereto by other means, such as viacoordinatized 3-D image sets, position-defining frames, or correlationwith imaged or tracked fiducials or markers. A great number of suchsystems are known, being described for example in U.S. Pat. No.5,967,980 and related patents of M. Ferre et al, U.S. Pat. No.5,307,072, and others, so the features of such systems will not befurther described here.

[0032] As relevant to a first aspect of the present invention, anelectromagnetic tracking system includes a magnetic field generator anda magnetic field sensor together with signal conditioning circuitry anda processor for processing the conditioned signals. The generator andsensor are also referred to as transmitter and receiver below. Ingeneral, a varying current injected into one coil assembly produces amagnetic field, and this field induces a voltage in the other coilassembly. The induced voltage V is proportional to the rate of change ofthe applied current I, with a constant of proportionality equal to Lm,the mutual inductance. According to one aspect of the invention, amagnetic tracking system is configured to apply the transmitter drivesignals and the induced receiver assembly signals to determine mutualinductances, from which the processor then determines thecoordinates—i.e., the position and orientation coordinates, or simply“P&O”—of one coil assembly of the system with respect to the other coilassembly.

[0033] For two closed circuits the mutual inductance is given byNeumann's formula, and is equal to an expression which depends only onthe geometry of the closed circuits (e.g., the coils), and not on theelectronics used to measure the mutual inductance. Since the mutualinductance L_(m) is a ratio independent of applied current, wave form orfrequency, it remains a well defined measurement parameter under a widevariety of conditions, offering improved performance in real operatingenvironments. With three transmitting coils and three receiving coils,nine mutual inductances provide an over-determined system for derivationof the position and orientation coordinates.

[0034] In some embodiments, the roles of transmitter and receiverassemblies may be interchanged, each comprising a substantiallyidentical three axis dipole coil assembly. Preferably these assembliesare built so the three coils of an assembly each exhibit the sameeffective area, are oriented orthogonally to one another, and arecentered at the same point. For many of the applications alluded toabove, the coils are quite small and ideally are small enough (comparedto the transmitter-receiver distance) that they may, as an initialapproximation, be considered to exhibit dipole behavior. However, moregenerally, the system includes embodiments discussed more fully below,wherein one or more of the coils are modeled or their signals processedas finite size transmitter or receiver.

[0035] It should be noted that the closed magnetic generating orreceiving circuit includes the coil, its connecting cable and someelectronics to which the cable is connected. In accordance with apreferred embodiment of the present invention discussed further below,contributions of these extrinsic or ancillary circuit elements arereduced or eliminated, permitting a simple and highly accurate model ofthe coil alone with a direct short across the coil leads.

[0036]FIG. 1 schematically illustrates a basic measurement system 1employed in a prototype embodiment. A transmitter assembly 10 is drivenby a transmitter driver 11 to produce a magnetic field, while a receiverassembly 12 responds to the magnetic field by producing induced signals,coupling the signals induced therein to a receiver voltage preamp 13 andan analog to digital converter 14. The transmitter assembly 10 andreceiver assembly 12 may, for example, each include three coils,oriented along respective spatial axes. The digitized values of thereceiver voltages from the digital converter 14 pass to a digital signalprocessing system 18 that may be implemented in or may interface with ahost processor 20 Values of the transmitter coil drive signals 14 arealso digitized by an analog to digital converter, and pass on line 15,to the digital signal processing system 18. In a preferred embodiment,the driver 11 applies known or approximately known voltages, rather thanknown or approximately known currents, to the transmitter assembly 10,and measures one or more currents induced in the coils of thetransmitter assembly. This voltage-driven approach advantageouslyalleviates the need to control the phase of one or more currents appliedto the transmitter coils, and further permits the system to functioneven with mistuned and/or non-orthogonal transmitter coils. Those havingordinary skill in the art will appreciate that the transmitter in asystem according to the teachings of the invention can also be driven bycurrents rather than voltages.

[0037] The various signals are transmitted, sampled, and combined andprocessed in coordination, for which operation a timing andsynchronization control unit 30 forms a number of basic synchronizedtiming signals to define or control, for example, the multiplexing ofsignals between the transmission and receiving coils, control timing ofthe digitizing circuits, control the analog-to-digital (ADC) samplingrate, and the processing of the digitized raw signals from the coils toproduce a processed raw data output. The host processor also operateswith the raw data to effect the computational algorithms for determiningcoordinates and correcting position and orientation determinations.

[0038]FIG. 2 shows a more detailed hardware block diagram of this aspectof a tracking system which, in accordance with the present invention, isconfigured to make a robust and accurate determination of mutualinductance of the various transmitter and receiver assembly coil pairs.That information is then applied as further described below to determinethe position and orientation coordinates of one assembly with respect tothe other. For simplicity, the same numerals as employed in FIG. 1 areused to designate the transmitter, receiver, host processor, digitalsignal processor and synchronization or control circuitry.

[0039] As shown in this embodiment, a clock generator circuit 30provides timing signals which are applied to different units foreffecting synchronized processing described further below. These unitsinclude a signal sampling analog-to-digital converter 1 14 a (sometimesreferred to as ADC 114 or simply an A/D unit, below), which digitizesthe signal values received from the receiver assembly and the drivesignal values sampled from the transmitter assembly; a digital-to-analogconverter (DAC) 114 b which converts digital drive waveform signals toanalog voltages for powering the amplifier which supplies transmitterdrive signals; and a digital signal processing unit 18 and wave formgenerator 40.

[0040] The wave form generator 40 is a digital frequency synthesizerthat generates digital values of a sine wave signal at one or moreselected frequencies. These may include, for example, a separatefrequency for driving each of the transmitter coils. These digitalvalues are converted to analog values by DAC 114 b, and are fed to apower amplifier and filter 50 for driving each transmitter coil.Advantageously, the power amplifier may be a voltage amplifier. Thedrive signal at any given time, is switched by a current multiplexer tothe appropriate coil, and simultaneously the induced voltages in thereceiving coils are demodulated at the frequency of the transmitteddrive signal. Meanwhile, the drive current to the transmitter assemblyis detected by a current sensor 51 a and is measured by currentmeasuring circuitry 60.

[0041] As further shown in FIG. 2, the receiver coil assembly includes acalibration transmitting coil 10 a fixed at a position close to thethree receiver coils of the assembly. Coil 10 a may be, for example,immovably secured in a fixed orientation relative to the three receivercoils in an integrated unit. The coil 10 a is operated to generate alocal magnetic field, oriented so that it induces calibration voltagesignals in each of the receiving coils. The drive current in this coilis also measured by the current measuring circuitry 60. Coil 10 a isenergized, as described further below in connection with determinationof mutual inductances, to effect normalization of the component signalsreceived in the three receiving coils R_(x), R_(y), R_(z). Thecalibration coil 10 a is driven by a calibration coil driver.

[0042] The receiver coils R_(x), R_(y), R_(z), provide their voltageoutputs to a preamp and filter 80, the output of which is fed to theanalog-to-digital converter ADC 114 a, as described above, to producedigital signal values for processing. Converter 114 a also receives asan input, the outputs of the current measuring circuitry 60, so that theADC 114 a provides digital values of both the calibration coil currentand the transmitter coil currents to the digital signal processing unit18. Coordination between the various transmitting, receiving, sensingand converting steps is carried out with timing signals from the clockgenerator circuitry 30. By way of example, clock circuitry 30 mayoperate with a 25 megahertz clock, dividing it down (e.g., by 256) toset an ADC sample rate of 97.65625 kilohertz, which is successivelydivided by 2, by 1440, and by 256 to provide sample rate framing signalsof 48.828125 kilohertz for the DAC, and end of cycle frame signal at33.90842 Hz for a sum of products (SOP) processing module implemented inthe signal processor DSP 18. Further frequency division may provide acurrent multiplexer cycle rate (for switching transmitter drive cyclesto different coils) of 0.13245477 Hertz, or other synchronized timingsignals as appropriate. Thus, operation of the various hardware unitsshown in FIG. 2 is synchronized by the clock generator circuit 30. Suchan exemplary timing unit is shown in FIG. 5E.

[0043] One of the clock signals is fed to a digital wave form generator40 that synthesizes three distinct drive frequencies for the x-, y- andz-transmitter coils. It will be understood that the digital wave formgenerator 40 may be implemented in the host processor 20. However, it ispreferably a specialized frequency synthesis chip or circuit, whichproduces a digital continuous sine wave of precise frequency and phase.As described further below, the different frequencies are used to driveindependent magnetic field generator coils, and corresponding signalsinduced in receiver coils are detected and processed in a simple digitaldemodulator, a sum-of-products processor. Preferably, the synthesizedfrequencies are integral multiples of the sum of products digital signalprocessing cycle rates (i.e., the cycle rates of the DSP unit 18) sothat the sine wave repeats exactly every SOP cycle with no discontinuitybetween cycles. The frequencies so generated are fixed, and the sinewave generator may be implemented in a known fashion by precalculatingsamples of the desired sign wave signals and storing the samples in aprogrammable read only memory (PROM). The PROM addresses are then drivenby signals from timing generating counters (not shown) so that the PROMoutputs the samples in the serial format required by thedigital-to-analog converter 114 b. Another PROM output may implement thedivide by 1440 control logic.

[0044] The digital output values of generator 40 are converted to adifferential analog voltage in the DAC circuitry 114 b, which may, forexample, be a 24-bit Deltasigma digital-analog-converter. Its outputanalog signal is amplified by the amplifier 50 which may, for example,be implemented with a low pass filter and a fixed gain differentialamplifier.

[0045] As is apparent from the circuitry described thus far, systems ofthe invention set out to measure both the transmitter coil drivecurrents and the receiver coil induced voltages. These areratiometrically combined to form mutual inductance measurements. Variousfurther construction details may be practiced in order to have thedetected signals represent as accurately as possible the desiredpositional field dependence. FIGS. 5A-5D illustrate further constructiondetails useful in preferred constructions of the transmitting andreceiving hardware.

[0046] As shown in FIG. 5A, each transmitting coil is driven by adifferential amplifier 50 that amplifies the analog-convertedsynthesized drive frequency signal. The r input of the differentialamplifier is connected to the low end of the transmitter coil (denoted Lin the Figure), which is also connected to a virtual ground. A coaxialcable 55 carries the drive signal to the high end of the transmittercoil L, thus avoiding introduction of electromagnetic fields due tocurrents within the drive cable. The virtual ground, although notexactly a ground voltage, is connected to the r input of the amplifier,thus ensuring that the actual voltage applied across the transmittercoil will not be affected by small stray voltages on the virtual ground.In this manner, a stable drive voltage is applied across the transmittercoil.

[0047] Further, because the impedance of the amplifier r input is highcompared to the impedance of virtual ground or real ground, and itscurrent signal is low, the current drawn through the r connection issubstantially less than (e.g., typically 10⁴ times less than) thecurrent through the coil itself. This small error may be estimated andcorrected mathematically in subsequent processing. Similarly, thecoaxial cable capacitance may shunt a small current around the coil;this current may also be estimated and corrected mathematically.

[0048] As further shown in FIG. 5A, as a coil is driven by the amplifier50, the coil current is sampled between the low end of the coil and ther terminal of the driving amplifier. The detected drive current isapplied together with induced receiver coil signals for the computationof mutual inductance.

[0049] In addition, as shown in FIG. 5B, a reference impedancemeasurement is also provided at the transmitter by having a defineddrive signal periodically switched through a reference impedanceZ_(ref). The impedance of Z_(ref) is much larger than the coil to coilmutual impedances, so the Z_(ref) driver provides a smaller current. Asseen in FIG. 5B, a resistor, R_(c), which is large compared to Z_(ref),converts the voltage output of the difference amplifier 50′ to a smallcurrent in Z_(ref). This connection, viz., the difference amplifierinput r, is grounded, rather than connected to the low end of Z_(ref),for two reasons. First, the input r draws a small current which issignificant compared to the current in Z_(ref). Second, the receivermeasurement channel responses to Z_(ref) are measured only when thecurrent through Z_(ref) is being measured by the current-measurementchannel. The reference impedance Z_(ref) may plug directly onto theconnectors on the receiver electronics board thus avoiding theintroduction of artifacts or the parasitic characteristics of cabling.In this embodiment, Z_(ref) is utilized only for determining the mutualinductances L_(cal) between the calibration transmitting coil 10 a (FIG.2) and the receiver coils at the time of manufacturing the receiverassembly. While tracking, the three L_(cal) values corresponding tomutual inductances between the calibration transmitting coil 10 a andeach of the three receiver coils are employed as mutual inductancestandards.

[0050] The overall arrangement of the transmitter section is shown inFIG. 5C. The driver/amplifier 50 is connected in turn to each of thecoils and referenced by a current- switching multiplexer (CMX) 60. Thevirtual grounds for all the transmitter coils go through a current-modeswitch matrix, that connects none or one transmitter coil current to theprimary winding (e.g., a single-turn primary) of a current transformerT_(c), while connecting all the remaining transmitter coils to thehigh-current transmitter-coil common-ground point t. The selectedcurrent thus goes through the primary of the current transformer T_(c)to the ground point t. A suitable current transformer T_(c) may have aprimary-to-secondary turns ratio of about 1:200. It operates to isolatethe large transmitter currents from analog ground of the receiverelectronics, accurately reducing the transmitter currents to valueswithin the range of the virtual-ground preamp, and minimizing thereflected virtual-ground impedance seen by the transmitter coils.

[0051] The mutual-impedance reference is preferably operated at a lowercurrent than the transmitter coils are operated, so themutual-impedance-reference current is switched in or out (as shown) onthe secondary side of the current transformer T_(c). Moreover, thesecondary of T_(c) is always in the circuit, to cancel effects due totransformer magnetizing current, so that the magnetizing current thenappears as just another constant complex gain error in thecurrent-measurement channel. Such constant gain errors cancel out indata-reduction calculations. In FIG. 5C, the op amp and resistor R_(f)form a virtual-ground current-input, voltage-output amplifier.

[0052]FIG. 5D provides an arrangement alternative to that shown in FIG.5C. In this alternative arrangement, three transformers (62, 64, 66) areutilized, and the current switches are connected to the secondarywindings of the transformers. The impedance variation seen by eachtransformer coil in the transformer primary circuit, as a result ofopening and closing the corresponding switch, is much lower than thevariation seen in the arrangement of FIG. 5C. In particular, thevariations are reduced by a factor equal to the square of thetransformer turns ratio. For example, the use of a turns ratio of 1:200in the arrangement of FIGS. 5D results in reducing the impedancevariations by a factor of 40,000 relative to that in the arrangement ofFIG. 5C.

[0053] In operation of the system, magnetic fields generated by thetransmitter coils induce voltage signals in the receiver coils, andthese are received and sampled to develop raw received signal values forthe processing. The voltage-input preamp and ADC channel for onereceiver coil L is shown in FIG. 5E. The voltage from the inductor L isapplied via a coaxial cable 55 to the differential-voltage-input preamp.The preamp output is applied to the input of an analog to digitalconverter, such as the above described 24-bit Deltasigma ADC, through apassive lowpass filter. The filter eliminates alias responses as well aseffects due to nonlinear ADC input currents. Use of a coaxial cable hasthe advantageous benefit that external electromagnetic fields can induceno potentials between the center conductor and the shield of the coaxialcable (assuming a perfectly-conducting shield). By contrast, aconventional twisted-pair cable may cancel effects due to uniformapplied electromagnetic fields, but can introduce extraneous signals inthe presence of gradient fields (such as spatially varying fields) areused in the system.

[0054] Thus, in the illustrated embodiment, there is one voltage inputchannel for each receiver coil, and a channel for the current preamp.

[0055] Overall operation 200 of the position sensing system proceeds asshown in FIG. 3. The transmitting x-, y- and z-coils T_(x), T_(y), T_(z)are driven to generate magnetic fields, and the voltages induced in thethree sensor receiver coils denoted R_(x), R_(y), R_(z) are measured. Inaddition, a reference magnetic field is generated in a calibration coil1 Oa coil fixed in or close to the receiving coil assembly. The currentsflowing through the transmitting coils and the current flowing throughthe calibration coil are each measured, and all the signals, includingthe received voltage signals in each receiver coil, are digitized andpassed to a signal processing unit described below more fully inconnection with FIG. 4. The ADC sampling is controlled by a commontiming generator so that the timing relationship between ADC samples andDAC samples is tightly controlled. A suitable timing module is shown inFIG. 5F, having the representative framing, cycle time and otherprocessing or sampling intervals described above. The ADC outputs, andtiming reference information from the timing generator pass to a digitalsignal processing system. The signal processing applies quadraturedemodulation (i.e., digital heterodyning at the driving frequency of thecurrently-actuated transmitting x-, y-, z- or calibration coil signal)to accumulate sum-of-products (SOP) complex raw signal values, andcomputes various matrices which allow one to normalize the couplingbetween the coils and the response of the receiver coils to thecalibration coil.

[0056] These are used in the next stage to form a nine element mutualinductance matrix for all of the (3) transmitter and (3) receiver coilpairs. The matrix is then used to compute coordinates of the receivercoil assembly with respect to the transmitter. The overall approach forthe latter computation may be similar to that employed in a conventionalfield model dipole approach, such as that described in the 1979 paper ofF. H. Raab et al. Volume AES-15, No.5, pp. 709-718, and Frederick H.Raab. Quasi-static Magnetic Field Technique for Determining Position andOrientation. IEEE Transactions on Geoscience and Remote Sensing. GE-19(4): 235-243, October 1981. For computation of position and orientationcoordinates, the processing preferably proceeds by starting with aninitial estimate of the six position and orientation coordinates,applying those coordinates to compute a mutual inductance matrix, anditeratively refining the coordinate estimate to enhance the goodness offit between the mutual inductance values as measured, and thosepredicted from the estimate.

[0057] As discussed further below, various features of the processingmake the mutual inductance model highly accurate and not prone to errorsof scale or position. Moreover since direct solutions are possible, theiteration proceeds quickly so that the position and orientationcoordinates may be output based on the estimated coordinates andmeasured mutual inductance matrix. Appendix A attached heretoillustrates a suitable calculation for deriving an initial set ofposition and orientation coordinates from a measured set ofdipole-modeled mutual inductances L_(tr) of the transmitter/receivercoil pairs. The dimensions of the coils are assumed to be small comparedto their separation, allowing derivation, for example, as described inthe paper of Frederick H. Raab. Quasi-static Magnetic Field Techniquefor Determining Position and Orientation. IEEE Transactions onGeoscience and Remote Sensing. GE-19 (4): 235-243, October 1981. Mutualinductances may be calculated for dipole coils or for circuits comprisedof straight line segments as outlined in Appendix B and Appendix C. Eachof the foregoing appendices is hereby incorporated herein by referenceand made a part of this description.

[0058]FIG. 4 is a block diagram showing the digital signal processing400 undertaken with the digitized coil drive currrent and sensingvoltage measurements. As shown, each of the signal measurements isdigitized in a high precision (24 bit) ADC. The signals are filtered andsynchronously quadrature demodulated, for example, using aDolch-Chebyshev FIR filter, and the complex signal values are thenapplied to construct three matrices 410, 420, 430 which are used todetermine the mutual inductances and to normalize measurements. Matrix410 is a raw signal matrix made of the signal components induced in eachof the receiver coils by each of the transmitter coils. Matrix 420 is a3×3 diagonal matrix, the three entries of which represent the responseof the respective receiver coils to the calibration coil. Matrix 430 isa 3×3 current matrix with entries representing the current through eachcoil (on the diagonal) and the current due to the other coils (off thediagonal). That is, it is a cross-coupling matrix. The DSP or processoralso computes the inverse 435 of this matrix, and the current throughthe calibration coil is provided as a separate parameter 440.

[0059] In general, the mutual impedance measuring system is designed formeasurement of small mutual impedances at frequencies between 100 Hz and40 kHz, and preferably between about 10 kHz and 15 kHz. The referenceimpedance Z_(ef).may be a 10 ohm ±100 ppm four-terminal resistor, sothat Z_(ref) is real and independent of frequency at the frequencies ofinterest. The whole system is ratiometric: the mutual impedances aremeasured with respect to Z_(ref) so that no precision voltage or currentreferences are required. Moreover, the frequency responses of thereceiver measuring channel and the current measuring channel are thesame, so that factors of the complex gains that vary with frequency willcancel in the ratioing process. Similarly, frequency-independent complexgain factors of the receiver measuring channels will also cancel in thedetermining the ratio of mutual impedances to Z_(ref).

[0060] Overall, the system operates by converting the raw signalmeasurements as discussed above to a mutual inductance matrix, and thensolving for position and orientation (P&O) from the mutual inductance.

[0061] The first step to computing P&O is converting sum-of-products(SOP) data into a normalized raw signal matrix (RSM) of mutualinductances. The SOP data is processed to preserve phase information, sothere is a real and an imaginary component of each parameter. Theunnormalized matrix has these complex entries., while, the mutualinductance matrix consists solely of real numbers. As discussed above,it is the end result of normalizing a complex signal matrix (CSM) forthe effects of current, coil and calibration coil response. The goal ofthis step is to end up with a 3×3 matrix containing the mutualinductances between all possible combinations of sensor and transmittercoils. Because there are three sensor and three transmitter coils, thereare a total of nine elements in the signal matrix. Each row of thematrix corresponds to a sensor coil and each column to a transmittercoil.

[0062] The RSM is computed by performing a series of matrixmultiplication operations. The effects of transmitter current arenormalized out (because the B field is directly proportional to thecurrent through the transmitter), as are the effects of frequency(db/dt) and receiver channel gain (using the calibration coil responsematrices). The formula is shown below:RSM(the  mutual  inductance  matrix)equals${ICM}*\begin{pmatrix}{{{Fcal}/F}\quad 0} & 0 & 0 \\0 & {{{Fcal}/F}\quad 1} & 0 \\0 & 0 & {{Fcal}/{F2}}\end{pmatrix}*{CSM}*\begin{pmatrix}{{Fcal\_ sop}{{\_ C}/{Fcal\_ sop}}\_ 0} & 0 & 0 \\0 & {{Fcal\_ sop}{{\_ C}/{Fcal\_ sop}}\_ 1} & 0 \\0 & 0 & {{Fcal\_ sop}{{\_ C}/{Fcal\_ sop}}\_ 2}\end{pmatrix}*\begin{pmatrix}{{cc\_ cf}\lbrack 0\rbrack} & 0 & 0 \\0 & {{cc\_ cf}\lbrack 1\rbrack} & 0 \\0 & 0 & {{cc\_ cf}\lbrack 2\rbrack}\end{pmatrix}$

[0063] where F0, F1, F2 are the frequencies of the x-, y- andz-transmitter coils, and where the complex entry Fcal_sop_C is themeasured sum-of-products current through the calibration coil,Fcal_sop_(—)0 is the response of the x-sensor coil to the calibrationcoil field, etc.

[0064] The above mutual inductance matrix is then applied to determinethe position and orientation coordinates of the coil assembly. Thisoperation proceeds by first obtaining a good estimate of P&O, forexample, by using the direct dipole solution of the Raab paper citedabove (which may be augmented to correct for coil size and known fielddisturbances). The processor first factors out the effects of gain &non-orthogonality of both the receiver and transmitter coils. This maybe done by pre-multiplying the RSM by the receiver gain matrix inverse,and post-multiplying by the inverse of the transmitter gain matrix.Detailed mathematical derivation of this method is given in the attachedAppendix A.

[0065] Specifically,

[0066]R=(Recr_gain_matrix⁻¹)*RSM*(Trans_gain_matrix⁻¹)

[0067] where R is now a 3×3 matrix where the effects of receiver andtransmitter gain and non-orthogonalities have been removed. One can nowestimate the range, r, (the square root of x²+y²+z²) and the magnitudeof the x,y,z coordinates based on the square of the total field from thethree transmitter coils.

[0068] The pertinent equations (1-4) are: $\begin{matrix}{r =^{6}\sqrt{6.0*{k^{2}/{Stotal}}}} & (1) \\{x = {{r^{4}/k}*\sqrt{\left( {{5.0*{Sx}} - {Sy} - {Sz}} \right)/18}}} & (2) \\{y = {{r^{4}/k}*\sqrt{\left( {{5.0*{Sy}} - {Sx} - {Sz}} \right)/18}}} & (3) \\{z = {{r^{4}/k}*\sqrt{\left( {{5.0*{Sz}} - {Sy} - {{Sx}/18}} \right.}}} & (4)\end{matrix}$

[0069] where, k is a scale factor that is the product of the area andnumber of turns of receiver and transmitter coils and permeability offree space. Stotal is the sum of signal matrix elements squared. Sx, Sy,Sz, are the sum of signal matrix elements squared for the XY,Ztransmitter coils, respectively.

[0070] Because of the hemispherical ambiguity associated with thetracker, the processor may always assume it is operating in the +Xhemisphere, and simply take dot products between sensor output vectors(the rows in a transposed signal matrix) to determine the sign of y andz.

[0071] However, the solution is unstable if any of the coordinate valuesis close to zero. (See Appendix A). To correct for this, the processorpreferably mathematically rotates the signal matrix elements to move thesolution into an optimal (non-zero) region which herein refers to aregion in which the numerical coordinate values are substantiallynon-vanishing such that a stable solution of the coordinate values canbe obtained by utilizing the above methodology The rotation isdetermined by computing the quaternion effective to move the initialposition estimate to an “ideal” solution location where x=y=z (i.e.,away from the x, y and z axes). This ensures that the solution isnumerically accurate and stable. The processor then recalculatesequations (1)-(4) with the rotated R matrix. After determining these“rotated” position coordinates, the processor de-rotates with theinverse quatemion to obtain a better estimate of the true position.Again, dot products are employed to determine the sign of thecoordinates.

[0072] The r, x ,y and z values are then used to compute 3×3 matricesTα, Tβ and their inverses. The matrices Tα, Tβ are rotation matricesbuilt from the (positional) spherical coordinates angles, α, β,respectively. Note, however, that because

cos(α)=x/sqrt(x ² +y ²)

sin(β)=z/r

[0073] Tα, Tβ and their inverses (Tα⁻¹, Tβ⁻¹) may be constructeddirectly from x,y, and z. These matrices along with the inverse of aconstant sensitivity matrix, S⁻¹, allow the inverse-coupling matrix, Q⁻¹(described in the aforesaid Raab paper) to be computed.

[0074] Basically,

Q ⁻¹ =Tα ⁻¹ *Tβ ⁻¹ *S ⁻¹ *Tβ*Tα  (5)

[0075] With Q⁻¹ and the signal matrix, R, the processor computes therotation matrix, A, that converts a zero-orientation sensor output intothe output of the true sensor:

A=(r ³ /k)*R*Q ⁻¹  (6)

[0076] where the elements of A can be described by a rotationquaternion, q=(qs,qx,qy,qz}:

A[0][0]=(qs ² +qx ² −qz ²),

A[0][1]=2*(qy*qx+qs*qz),

A[0][2]=2*(qz*qx−qs*qy),

A[1][0]=2*(qy*qx−qs*qz),

A[1][1]=(qs ² −qx ² +qy ² −qz ²),

A[1][2]=2*(qz*qy+qs*qx),

A[2][0]=2*(qz*qx+qs*qy),

A[2][1]=2*(qz*qy−qs*qx),

A[2][2]=(qs ² −qx ² +qy ² +qz ²).

[0077] The elements of A may be used to find a rotation quaternion, ‘q’,using the procedure in Appendix A8 of the paper of B. Horn, Closed-formsolution of absolute orientation using unit quaternions, J. Opt. Soc.Amer. Vol 4. p 629, April, 1987. Note, however, that here A is theinverse of the rotation matrix described in that paper.

[0078] The foregoing procedure provides a very good estimate for theposition and orientation of the sensor. To refine the estimate ofposition and orientation, the processor next applies a fitting, such asa first-order or least square algorithm, to create a best-fit between aset of model estimated mutual inductances and the measured mutualinductances in the RSM. The idea is to compute a set of small correctionvalues to apply to the estimated P&O. The basic equation is:

E+S*(delta _(—) P _(—) O _(—) vector)=R

[0079] where

[0080] R is the measured signal matrix, formulated as a nine elementvector;

[0081] E is an estimated signal matrix computed using both the directsolution P&O estimate and a magnetic field model based on the actualgeometry of the coils employed in the system (where the signal matrix Eis also formulated as a nine element vector);

[0082] S is a 9×6 sensitivity matrix which holds the partial derivativesof signal matrix elements with respect to six position and orientationparameters (x,y,z,qx,qy,qz); and delta_P_O vector is the 6 element deltacorrection vector (Δx, Δy, Δz, Δqx, Δqy, Δqz) that is to be solved for.

[0083] The fourth component of the delta quaternion, Δqs, may be solvedfor by normalizing it to unit length.

[0084] Note that because the matrix S is not square, it cannot beinverted. However, to put it into an invertible form, one can multiplyit by its transpose (ST). See, for example, W. Brognan. Modern ControlTheory. Prentice-Hall, 1991, pp 222-223. The least squares equation weend up with is:

delta _(—) P _(—) O _(—) vector=[Δx,Δy,Δz,Δqx,Δqy,Δqz] ^(T)=(S ^(T) *S)⁻¹*(S ^(T))*(R−E)

[0085] Finally, sensor position is adjusted by:

x=x+Δx; y=y+Δy; z=z+Δz

[0086] and the sensor orientation (as a quaternion), qorient, isadjusted by rotating it by the computed delta quaternion, qdelta:

qorient=qdelta*qorient

[0087] Thus, the processor operating with SOP data from the magnetictracking units computes and refine the position and orientation of themovable coil assembly.

[0088] As noted above, certain structures present in the tracking arenamay introduce field distortions because eddy currents induced inconductive structures will themselves generate magnetic fields. Inaccordance with other aspects of the invention, this problem isaddressed in one or more of several ways.

[0089] One of these ways is to mount the receiver (sensor) of the systemon or close to a major interfering structure, such as (in a medicalcontext) the C arm of a fluoroscope assembly. The transmitter coilassembly is then the movable assembly of the tracker, and will thus begenerally positioned remotely from the interfering structure. The mutualinductance tracker of the invention can be configured to operateeffectively with small coils which may be carried by a hand-held tooland the like, thereby rendering the above approach feasible. Further,the use of mutual inductance between the transmitter and receiver unitsin the electromagnetic tracker of the invention allows swapping thefunctionality of the transmitter and receiver units, e.g., utilizing anominal sensor coil as a transmitter and/or a nominal transmitter coilas a receiver. This reciprocity can be particularly advantageousbecause, in some cases, it may be more convenient to map and/or modelthe field generated by one unit, e.g., receiver, rather than the other,e.g., transmitter.

[0090] Another aspect of the invention dealing with the fielddisturbance problem is to mount a standardized conductor about such aninterfering structure to operate as a shield (e.g., with respect todisturbances originating within the shield) and a known disturber, asseen by a sensor positioned outside the shield. The standardizedconductor, such as a metal can, then has a fixed position relative toone of the coil assemblies, and may be effectively modeled. Thus, theeddy currents induced in the sheet metal cylinder by the magnetic fieldfrom the transmitter assembly, and the secondary B field formed by theseinduced currents, may be modeled such that the processor can applydeterminable field contributions from the shield. Without such a shield,applicant has found that when a coil assembly is employed in proximityto certain interfering structures (such as the imaging assembly of afluoroscope), the disturbance caused by that structure may varyconsiderably for two different but apparently identical units. Theshield moderates such differences; electromagnetic fields originatingwithin the shield are largely null outside the shield. Moreover, littleof the tracking signal origination outside the shield penetrates inside,so that the level of eddy currents induced in the structural conductiveelements inside the shield are subject only to quite low fields andtheir eddy currents and secondary field effects are greatly diminished.These combined effects allow a tracking system to operate effectively byapplying standardized (modeled or calibrated) corrections for the shieldalone, without regard to the specific structure(such a s a fluoroscopeimaging assembly) that it isolates.

[0091] Preferably, the shield is made of a single piece of a highlyconducting material, e.g., a metal such as silver, copper or aluminum,or a conductive composite. The shield surrounds the targeted componentor piece of interfering equipment, such as the image intensifierassembly of a fluoroscope, as much as possible, consistent with systemconstraints (e.g., X-ray transparency of the top end, mechanicalprotrusion limits for camera movement, etc.). Preferably, the shieldthickness is sufficient, e.g., more than the skin depth of the metal ormore than several skin depths, so that the magnetic field it generateswill not appreciably penetrate the shield or extend into the volumebehind the shield.

[0092] The field distortions introduced by the shield may be mapped anda tracker-correction table may be generated in a preliminary set-up orcalibration step, or the effect of the shield may be modeled.

[0093] The shield greatly reduces the magnitude of equipment-relatedmagnetic field distortion reaching the targeted structure, andintroduces its own, highly determined effects. Thus, as applied, forexample to a fluoroscope, changing the image intensifier has noappreciable effect on the resulting field distortion, and one fielddistortion correction table can be used for all image intensifiers of agiven model, and sometimes even for image intensifiers of differentmodels.

[0094]FIG. 6 illustrates such a system in an embodiment 10 for use insurgical navigation in an operating room environment. As shown, thesystem 10 includes a fluoroscope 20, a work station 30 having one ormore displays 32, 33 and a keyboard/mouse or other user interface 34,and a plurality of tracking elements T1, T2, T3. The displays mayillustrate imaged views or synthesized views 40′ of tool trajectories,tissue or the like. The fluoroscope 20 is illustrated as a C-armfluoroscope in which an x-ray source 22 is mounted on a structuralmember or C-arm 26 opposite to an x-ray receiving and detecting unit,referred to herein as an imaging assembly 24. The C-arm moves about apatient for producing two dimensional projection images of the patientfrom different angles. The patient remains positioned between the sourceand the imaging assembly 24, and may, for example, be situated on atable 14 or other support. The patient may be secured in a fixedposition on the support and the support may be tracked, or moretypically, the patient may be movably positioned. In the latter case,tracking elements T3 may be affixed to one or more relevant portions ofthe patient's body. In the illustrated system, tracking elements aremounted such that one element T1 is affixed to, incorporated in orotherwise secured against movement with respect to a surgical tool orprobe 40. A second tracking unit T2 is fixed on or in relation to thefluoroscope 20, and a third tracking unit T3 is shown fixed on or inrelation to the patient. The surgical tool may be a rigid probe as shownin FIG. 6, allowing the tracker T1 to be fixed at any known orconvenient position, such as on its handle, or the tool may be aflexible tool, such as a catheter, flexible endoscope or an articulatedtool. In the latter cases, the tracker T1 is preferably a small,localized element positioned in or at the operative tip of the tool asshown by catheter tracker T1′ in FIG. 6, to track coordinates of the tipwithin the body of the patient.

[0095] As will be understood by those having ordinary skill in the art,fluoroscopes typically operate with the x-ray source 22 positionedopposite the camera or image sensing assembly 24. While in some systems,the X-ray source is fixed overhead, and the camera is located below apatient support, the discussion below will be illustrated with regard tothe more complex case of a typical C-arm fluoroscope, in which thesource and camera are connected by a structural member, the C-arm 26,that allows movement of the source and camera assembly about the patientso it may be positioned to produce x-ray views from different angles orperspectives. In these devices, the imaging beam generally diverges atan angle, the relative locations and orientations of the source andcamera vary with position due to structural flexing and mechanicallooseness, and the position of both the source and the camera withrespect to the patient and/or a tool which it is desired to track mayall vary in different shots. Thus, the use of one or more trackingelements T3 (transmitters or receivers) on the structure itself may beuseful to quantify these movements in the surgical navigation system.Further details of this complex imaging environment may be found incommonly owned U.S. patent application Ser. Nos. 09/560,940 and09/560,608, both filed on Apr. 28, 2000, and each of which isincorporated herein by reference. Each of those patent applicationsdiscloses a tracking system wherein tracking of the fluoroscope as wellas the tool and patient produce image sets and surgical navigation ofenhanced accuracy.

[0096] The imaging beam illustrated by B in FIG. 6 diverges from thesource 22 in a generally truncated conical beam shape, and the C-arm 26is movable along a generally arcuate path to position the source andcamera for imaging from different directions. This generally involvespositioning the assembly 24 as close as possible behind the relevanttissue or operating area of the patient, while the C-arm assembly ismoved roughly about a targeted imaging center to the desired viewingangle. The C-arm or other beam structure 26 may move eccentrically ortranslationally to allow better clearance of the patient support table,but generally, the camera assembly 24 is positioned close to site ofsurgical interest. Because, as noted above, the camera 24 may utilize animage sensing unit that introduces distortions into electromagneticfields employed for tracking, this complicates the task of tracking,particularly in view of the proximity of the disturber to the trackingsensors positioned on the patient or the surgical tool.

[0097] As further shown in FIG. 6, this problem is advantageouslyaddressed by providing a conductive shield/distorter 25 surrounding theimage assembly 24, which may be a metal or conductive cylinder.Preferably the top face is open, so as to avoid degrading the X-rayimage or contrast detected by the assembly 24. Most preferably, theelectromagnetic tracking element T3 is a sensor element, rather than atransmitter, and it is mounted in a fixed position in relation to theshield 25. That is, the tracking element T3 is clamped to the shield 25,or clamped to the C-arm (as illustrated) or to the imaging assemblyclose to the shield. This device architecture is advantageously used inconnection with a processor to achieve enhanced speed and robustness ofthe tracking coordinates.

[0098] As discussed above, in a tracker of the invention, a shield maybe modeled in the processor, so that a more accurate model of themagnetic field data is present initially, either obviating or reducingthe task of actually mapping the disturbed field measurements. When theprocessor determines position and orientation components by refining aniterative estimation or fitting procedure, for example wherein thesystem estimates the coordinates of a transmitter or sensor unit, or therelative coordinates by comparing calculated signal measurements withmeasured signal values, such modeling may produce faster and lesscomputationally intensive convergence of the fitting procedure. Thus,for example, a cylindrical “can” fitted about the imaging assembly of afluoroscope may be effectively modeled as a conductive ring or annulusat the defined position. This may produce a kernel or an initial seedsolution without resorting to massive stored field calibration tables,or may yield a fast or even closed form calculation of the fielddistribution for P&O determination. A traditional approach to the designof electromagnetic trackers set forth, for example, in the 1981 paper ofF. H. Raab, supra, assumes magnetic dipole field distributions for boththe transmitting and sensing coils. This assumption permits an analyticsolution for position and orientation coordinates (hereinafter, simply“P&O”) based on the measured sensor data. However, in cases where theactual fields deviate from the dipole form, application of adipole-based algorithm produces distorted P&O estimates. Such deviationsoccur, for instance, when coil sizes are significant relative to thesource-sensor separation distance, or when conducting or magneticmaterials are located near the sensors. (The term sensor is used hereinto refer to both transmitting and receiving coils unless specificallynoted). An analytic solution for P&O is not generally possible fornon-dipole field models, so in order to continue to use this formalismin the presence of real fields, a typical approach has been to correctthe P&O estimates from the dipole algorithm using a large lookup tablecontaining measured values of the distortion over the working volume, asdescribed in Zachman, G. Distortion Correction of Magnetic Fields forPosition Tracking. Proc. Computer Graphics Int'l (CGI'97), Jun. 23-27,1997, Hasselt & Diepenbeek, Belgium.

[0099] However, in accordance with another aspect of the presentinvention, rather than proceeding by creating a distortion map for everyapplication, a system implements a P&O determination based on a moreaccurate model of the sensor field (for example, modeling the extrinsicdistortion) that eliminates the need for a map by curing the distortionproblem at its source.

[0100] Numerical models (e.g., finite element methods) can be madearbitrarily accurate, but the computational cost for this accuracy maybecome quite high. As an alternative, a given source may be approximatedas a collection of simple shapes for which the fields can be expressedanalytically. This approach provides a compromise between accuracy andspeed, where the accuracy will be limited by the ability to match theactual geometry with a set of simple shapes, which determine the “basicfunctions” for the expansion.

[0101] This approach has been applied in a further aspect of theinvention to a fluoroscopic tracking system where the sensor is mountedclose to a large parasitic element, namely the C-arm of a fluoroscope.In this case, a distorter element, for example, in the form of a largemetal can is preferably mounted on the C-arm image intensifier todominate the field distortion. The sensor fields are then modeled as athree-axis dipole located near a filamentary conducting ring. The fieldsof both a dipole and filamentary ring can be computed analytically (see,for example, Smythe, WR. Static and Dynamic Electricity. HemispherePublishing, New York, 1989. A composite model of the coupling matrixcomponents can therefore be written as the sum of analytic expressions.The following sections describe the model in detail.

[0102] To embed the new field model in the tracker fit routine, oneneeds a way to compute the coupling matrix between the transmitter andreceiver in the presence of the distortion source. To accomplish this,applicant makes two assumptions:

[0103] (i) Assume that the transmitting and receiving sensor coils canbe modeled as magnetic dipole elements. This assumption allows for aconvenient dot product relationship between the field vector and inducedvoltages, as the coils are assumed to be point sources/receivers.

[0104] (ii) Assume that the dominant distorter is the metal can aroundthe image intensifier, and that we can model that can as a simple metalring. This assumption allows us to use analytic expressions for themagnetic fields radiated by the ring, which are available in theliterature (Smythe, supra or Jackson, JD Classical Electrodynamics.Wiley, New York, 1975).

[0105] Using these assumptions, the development proceeds as follows.First, use network theory to derive an expression for the couplingbetween the transmitter and receiver in the presence of the ring. Thisexpression contains several mutual and self-inductance terms that weneed to compute. Known expressions for the coupling between two dipoleelements are used together with the fields generated by a ring tocompute the required inductances. Finally, the signal matrix elementscan be computed as a function of P&O.

[0106] The voltage induced on a receive coil due to a current flowing ona transmit coil in the presence of a metal-ring can be computed byconsidering the system as a three-port network, as schematically shownin FIG. 7.

[0107] The impedance parameters describing the coupling among the portsare given by: ${\begin{bmatrix}V_{1} \\V_{2} \\V_{3}\end{bmatrix} = {\begin{bmatrix}Z_{11} & Z_{12} & Z_{13} \\Z_{21} & Z_{22} & Z_{23} \\Z_{31} & Z_{32} & Z_{33}\end{bmatrix} \cdot \begin{bmatrix}I_{1} \\I_{2} \\I_{3}\end{bmatrix}}},{{{where}\quad Z_{ij}} = {\frac{V_{i}}{I_{j}}_{I_{k \neq j} = 0}}}$

[0108] (See, e.g., Pozar, D M. Microwave Engineering. Addison-Wesley,Reading, Mass., 1990.)

[0109] Consider the case where we want to know the voltage induced onport 2 (the receiver) when port 1 (the transmitter) is driven with afixed voltage, port 2 is loaded with an impedance Of Z_(L), and port 3(the ring) is loaded with a short circuit. After some algebra, we canwrite the induced voltage on port 2 relative to the current through portI as: $\begin{matrix}{\frac{V_{2}}{I_{1}} = {\left\lbrack {{j\quad \omega \quad L_{12}} - \frac{\left( {j\quad \omega \quad L_{13}} \right)\left( {j\quad \omega \quad l_{23}} \right)}{Z_{33}}} \right\rbrack \cdot {\left\lbrack {1 + \frac{\left( {j\quad \omega \quad L_{23}} \right)^{2}}{Z_{33} \cdot Z_{L}} - \frac{Z_{22}}{Z_{L}}} \right\rbrack^{- 1}.}}} & \left( {{Eq}.\quad 5} \right)\end{matrix}$

[0110] If we assume that Z_(L) is “large” relative to the other terms inthe second set of brackets, and that the resistance of the ring isnegligible, Equation 5 reduces to:$\frac{V_{2}}{I_{1}} \cong {{j{~~}\omega \quad L_{12}} - \frac{\left( {j\quad \omega \quad L_{13}} \right)\left( {j\quad \omega \quad L_{23}} \right)}{L_{33}}}$

[0111] This approximation is sufficient for many cases, and the fullexpression in (5) can be implemented where the additional accuracy isrequired.

[0112] To calculate the mutual inductance between the transmitting orreceiving coils and the ring, we apply reciprocity and let the ring actas the source for both cases. By first calculating the field radiated bya current flowing on the ring, the voltage induced at the transmit orreceive coil is given by a simple dot product. Under the magneto-staticapproximation, the B-field produced by a uniform current I flowing on afilamentary ring (FIG. 8) is given in cylindrical coordinates by Eq.(7):${B_{\rho} = {\frac{\mu \cdot I}{2\pi} \cdot \frac{z}{\rho \cdot \left\lbrack {\left( {a + \rho} \right)^{2} + z^{2}} \right\rbrack^{1/2}} \cdot \left\lbrack {{- K} + {\frac{a^{2} + \rho^{2} + z^{2}}{\left( {a - \rho} \right)^{2} + z^{2}} \cdot E}} \right\rbrack}},{B_{z} = {\frac{\mu \cdot I}{2\pi} \cdot \frac{1}{\left\lbrack {\left( {a + \rho} \right)^{2} + z^{2}} \right\rbrack^{1/2}} \cdot \left\lbrack {{- K} + {\frac{a^{2} - \rho^{2} - z^{2}}{\left( {a - \rho} \right)^{2} + z^{2}} \cdot E}} \right\rbrack}},{B_{\varphi} = 0},$

[0113] where K and E are complete elliptic integrals of the first andsecond kind, respectively, and the argument k for the integrals is givenby

4aρ·[(a+ρ)² +z ²]⁻¹.

[0114] Equation 5 requires the computation of one self inductance termand three mutual inductance terms (additional terms must be calculatedfor Equation 6, which makes no approximations).

[0115] The self-inductance term is for the ring, and is given by [7]${L_{ring} = {a \cdot \left\lbrack {{\mu \cdot \left( {{\ln \frac{8a}{b}} - 2} \right)} + {\frac{1}{4}\mu^{\prime}}} \right\rbrack}},$

[0116] where

[0117] a is the radius of the loop,

[0118] b is the radius of the wire,

[0119] μ′ is the permeability of the wire material, and

[0120] μ is the permeability of free space.

[0121] The mutual inductance L₁₂ between the transmitting and receivingcoils is derived in [10] using the dipole assumption, and can becalculated as$L_{12} = {\frac{\mu_{0}A_{1}A_{2}}{4{\pi \cdot R^{3}}} \cdot {\left\lbrack {{3 \cdot \left( {{\hat{A}}_{1} \cdot \hat{R}} \right) \cdot \left( {\hat{R} \cdot {\hat{A}}_{2}} \right)} - \left( {{\hat{A}}_{1} \cdot {\hat{A}}_{2}} \right)} \right\rbrack.}}$

[0122] where

[0123] {overscore (A)}₁=effective area of the transmitting dipole,

[0124] Â₁=unit vector in the direction of {overscore (A)}₁,

[0125] A₁=magnitude of {overscore (A)}₁,

[0126] {overscore (A)}₂=effective area of the receiving dipole,

[0127] A₂=unit vector in the direction of {overscore (A)}₂,

[0128] Â₂=magnitude of {overscore (A)}₂.

[0129] {overscore (R)}=the vector from the transmitter to the receiver

[0130] {circumflex over (R)}=the unit vector in the direction of{overscore (R)}

[0131] R=the magnitude of {overscore (R)}.

[0132] Given a position and orientation of the sensor relative to thetransmitter, the range R can be calculated. The effective area terms arecalculated based on the coil geometry and a calibration procedure [11].

[0133] The remaining two mutual inductance terms, those between thetransmitting coil and the ring, and between the receiving coil and thering, may be calculated in a similar manner.

[0134] The position and orientation of the ring relative to the sensorcoils is assumed to be known and fixed. Therefore, to compute the mutualinductance L₂₃ in Equation 6, first compute the P&O of the sensor in thecoordinate frame of the ring shown in FIG. 8. Next, compute the magneticfield per unit current produced by the ring at the sensor location.Finally, the mutual inductance term is calculated for each sensor coilby taking the dot product between the coil vector and the field, usingthe point source property of the dipole approximation.

[0135] Computing the mutual inductance between the transmitter and thering requires one additional step. Given the P&O of the sensor in thetransmitter coordinate system, we first convert so that we have the P&Oof the transmitter in the sensor coordinate frame. The procedure thenproceeds as above. The mutual inductance L₁₃ is computed by calculatingthe P&O of the transmitter in the ring coordinate system. Therelationship between the ring and the sensor is known and fixed as notedabove, so once the transmitter P&O is known relative to the sensor,conversion transformations are obvious. Next compute the magnetic fieldper unit current produced by the ring at the sensor location. Finally,the mutual inductance term is calculated for each sensor coil by takingthe dot product between the coil vector and the field, using the pointsource property of the dipole approximation.

[0136] With all of the inductance terms available, Equation 6 is thenreadily calculated. Overall, the approach of measuring mutualinductances allows the system to develop robust measurements in whichreliance on references such as Z_(ref) or a signal ratio, or use of acommon preamplifier with high precision output digitization, haveeliminated numerous sources of variability while allowing effective useof small magnetic assemblies to achieve accuracy and resolution.

[0137] Moreover, by introducing a shield or virtual distorter and fixinga receiver assembly with respect to the shield, the effects ofindividual distortion environments are substantially eliminated, and theshield itself may be effectively modeled, eliminating the cumbersomerequirement of compiling a mapping or calibration table. The model maythen produce a seed calculation, allowing computationally effectivefitting processes to replace the cumbersome calculations of the priorart. In other words, a distorter that is shaped to optimally shieldmagnetic fields from existing environmental distorters can be utilizedwithout any regard for a specific desired field shape. The shield'seffect on the field can then be modeled, or alternatively, mapped.

[0138] The invention being thus disclosed and illustrative embodimentsdepicted herein, further variations and modifications of the inventionwill occur to those skilled in the art, and all such variations andmodifications are considered to be within the scope of the invention, asdefined by the claims appended hereto and equivalents thereof.

What is claimed is:
 1. An electromagnetic tracking system comprising amagnetic field generating unit driven by a drive signal, a field sensingunit having a sensing signal responsive to changing magnetic field thegenerating and sensing units being arranged to generate and to sense,respectively, an electromagnetic field in an arena of interest, andwherein at least one of said units is movable, signal measurement andconditioning circuitry connected to said units to (i) detect the drivesignal and the sensing signal, (ii) ratiometrically combine said signalsto form a mutual inductance matrix, and a processor operative with themutual inductance matrix to determine coordinates of the movable unit.2. The electromagnetic tracking system of claim 1, wherein said systemdrives the field generating unit with a controlled voltage drive line,and senses current in said line.
 3. The electromagnetic tracking systemof claim 1, wherein said field generating unit comprises a plurality ofindependent field coils, a multiplexer coupled to said coils forselecting any one of said coils, and an amplifier coupled to said coilsvia the multiplexer, the amplifier measuring a current flowing throughany of the coils selected by the multiplexer.
 4. The electromagnetictracking system of claim 1, further comprising a calibrationtransmitter, the calibration transmitter being fixed with respect to thefield sensing unit for generating a fixed reference field sensed by saidsensing unit.
 5. The electromagnetic tracking system of claim 4, whereinthe field sensing unit comprises n≧2 coils spanning n≧2 dimensions, andthe calibration coil is positioned to couple signal into each of saidcoils.
 6. The electromagnetic tracking system of claim 4, furthercomprising a current sensor that senses one or more currents induced inthe generating unit by the drive signal and another current sensorsenses current in the calibration transmitter, both said current sensorsbeing coupled to a common amplifier thereby providing a common gainfactor for all current measurements
 7. An electromagnetic trackingsystem comprising a magnetic field generating unit having at least onefield generating coil driven by a drive signal, a field sensing unithaving at least one field sensing coil generating a sensing signalresponsive to a changing magnetic field, said changing magnetic fieldincluding a position-dependent field produced by said magnetic fieldgenerating unit the generating and sensing units being arranged togenerate and to sense, respectively, an electromagnetic field in anarena of interest, and wherein at least one of said units is movable,signal measurement and conditioning circuitry connected to said units to(i) synchronously sample and digitize drive signal data and sensingsignal data for respective pairs of field generating and field sensingcoils, cumulating the digitized data to form a raw signal matrix, and(ii) determine a mutual inductance matrix from the raw signal matrix,and a processor that utilizes the mutual inductance matrix to determinecoordinates of the movable unit.
 8. The electromagnetic tracking systemof claim 7, wherein the field sensing unit is fixed to a structure andthe field generating unit is movable.
 9. The electromagnetic trackingsystem of claim 7, wherein the processor normalizes the raw signalmatrix with respect to drive signal and sensing unit coil couplingresponse.
 10. The electromagnetic tracking system of claim 8, whereinthe processor determines coordinates of the movable unit byapproximating coordinates of the field sensing unit relative to thefield generating unit, and iteratively adjusting the approximatedcoordinates to determine coordinates of the movable unit.
 11. Theelectromagnetic tracking system of claim 7, wherein the drive signal isany of a drive current or a drive voltage.
 12. An electromagnetictracking system comprising a magnetic field generating unit driven by adrive signal, a field sensing unit having a sensing signal responsive toa changing magnetic field, said changing magnetic field including aposition-dependent field produced by said magnetic field generatingunit, the generating and sensing units being arranged to generate and tosense, respectively, an electromagnetic field in an arena of interest,and wherein at least one of said units is movable, signal measurementand conditioning circuitry connected to said units to sample anddigitize signal data for the field generating and field sensing units, adistorter having a known structure disposed at a selected location inthe arena of interest, and a processor operative on the sampled anddigitized signal data to determine relative coordinates and orientationsof said field generating or field sensing unit, said processor modelingthe distorter and the generating and sensing units to generate modeledsignal data and fitting said modeled signal data to measured signalvalues to determine coordinates and orientations of said fieldgenerating and field sensing units.
 13. An electromagnetic trackingsystem comprising a magnetic field generating unit and a magnetic fieldsensing unit, at least one said units being movable relative to theother, the sensing unit having a sensing signal responsive to a changingmagnetic field produced by said magnetic field generating unit thegenerating and sensing units being arranged to generate and to sense,respectively an electromagnetic field in an arena of interest, signalmeasurement and conditioning circuitry connected to said units to sampleand condition field generating and field sensing signal values aprocessor operative on sampled and conditioned signal values todetermine relative position and orientation of said units wherein thesignal measurement and conditioning circuitry includes a common gainstage amplifier connected to plural coils and a high precision analog todigital converter that converts amplified coil signals to high precisiondigital values such that coil outputs over a work arena may be digitallyprocessed without patching or conversion of gains in different regionsof the work arena.
 14. An intra-operative imaging and tracking systemfor guiding a surgical tool during a surgical procedure performed on apatient, comprising a fluoroscope having an x-ray source and an imagingassembly, said source and imaging assembly being movable about thepatient to generate a plurality of two-dimensional x-ray images of thepatient from different views, a magnetic tracker having a fieldgenerating unit driven by a drive signal to generate an electromagneticfield in an area of interest and a sensing unit that generates a sensingsignal in response to said field, one of said units being securedagainst movement relative to said imaging assembly and the other unitbeing affixed to the surgical tool, a magnetic field distorter securedagainst movement relative to said imaging assembly, a signal measurementcircuit for measuring said drive and sensing signals to generatemeasured signal data, and a processor operative on said x-ray images andsaid measure signals, said processor modeling said field distorter andsaid generating and sensing units to derive modeled signal data andfitting said modeled signal data to said measured signal data todetermine relative coordinates and orientations of said generating andsensing units, said processor further utilizing said x-ray images andsaid relative coordinates and orientations to determine position of thetool relative to the patient.
 15. An intra-operative imaging andtracking system for guiding a surgical tool during a surgical procedureperformed on a patient, comprising a fluoroscope having an x-ray sourceand a detector, said x-ray source and detector being movable relative tothe patient so as to generate a plurality of two-dimensional x-rayimages of the patient from different views, a magnetic tracker having amagnetic field generating unit driven by a drive signal to generate anelectromagnetic field in an area of interest and a magnetic fieldsensing unit generating a sensing signal responsive to theelectromagnetic field, one of said units being secured against motionrelative to the detector and the other unit being affixed to thesurgical tool, a signal measurement circuitry electrically coupled tothe tracker to measure said drive and sensing signals to form a matrixrepresenting mutual inductance between said generating and sensingunits, a processor operative with said mutual inductance matrix and saidx-ray images to determine coordinates of the unit affixed to thesurgical tool and position of the surgical tool relative to the patient.16. An electromagnetic tracking system comprising a magnetic fieldgenerating unit driven by a drive signal, a field sensing unit having asensing signal responsive to a changing magnetic field, said changingmagnetic field including a position-dependent field produced by saidmagnetic field generating unit, the generating and sensing units beingarranged to generate and to sense, respectively, an electromagneticfield in an arena of interest, and wherein at least one of said units ismovable, signal measurement and conditioning circuitry connected to saidunits to sample and digitize signal data for the field generating andfield sensing units, a distorter having a structure optimal forshielding one or more objects in the arena of interest, said distortedbeing disposed so as to substantially shield magnetic fields generatedby said objects, and a processor operative on the sampled and digitizedsignal data to determine relative coordinates and orientations of saidfield generating or field sensing unit, said processor modeling thedistorter and the generating and sensing units to generate modeledsignal data and fitting said modeled signal data to measured signalvalues to determine coordinates and orientations of said fieldgenerating and field sensing units.